In the context of tai chi push hands, what are the most commonly effective techniques? (Push hands in competition and in class both count.)

For analogy, in judo, it is well known and documented that the strongest players at the international level win most commonly with throws like osotogari, seoinage, and uchimata, whereas haraitsurikomiashi and udegatame, for instance, are seen much less often and mastered by fewer practitioners.

What are the high-percentage techniques of tai chi push hands, that nearly all players employ, or that many players employ to great effect?

3 Answers
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Needle at Sea Bottom is a fave for fixed feet push hands. Personally, I dont like the move but have been on the receiving end enough to know its effective in competition.

You can see it in this video at about 33 seconds in. The initial body and hand positioning is reasonably close to tournament and you can see the hip turn whilst sliding the weight backwards and controlling the opponents arm to throw them to the side. With fixed feet push hands, all you need to do is uproot and this move is often used very quickly from the start of the point.

A counter to it is to relax the arm being pulled, initially going with the movement (in the example above the hips would be rotating around to the left) but then rotate the hips to the right, slapping with the pulled hand followed up by a push with the left hand. Or just relax right out of the initial hold and help your opponent continue his movement backwards.

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Awesome! Could you give some detail on how its applied? Do you have maybe an example? (An image or video would be super-swell.)
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Dave LiepmannJun 5 '12 at 2:55

Hi Dave - this is the best example I could find at about 33 secs in. The initial body and hand positioning is reasonably close to tournament and you can see the hip turn whilst sliding the weight backwards and controlling the opponents arm to throw them to the side. With fixed feet push hands, all you need to do is uproot and this move is often used very quickly from the start of the point.
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Doug McKJun 6 '12 at 0:36

A counter to it is to relax the arm being pulled, initially going with the movement (in the example above the hips would be rotating around to the left) but then rotate the hips to the right, slapping with the pulled hand followed up by a push with the left hand. Or just relax right out of the initial hold and help your opponent continue his movement backwards.
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Doug McKJun 6 '12 at 0:37

The real Taijiquan skill is invisible. The application of Taijiquan is to be found in
understanding of insubstantiality, formlessness, and mind alone. The taste and feel of real
Taijiquan cannot be had from any application of visible technique or obvious force. That just
drifts you farther and farther from the real art of Taijiquan.

Perhaps this means that Taijiquan does not attach itself to particular techniques. The most popular skill, then, would be no-mindedly leading the opponent to unbalance.

This question definitely comes mc-dojo side of taichi. Look at Yang Family description of Yang Shou Hao:

"He developed a form that was high with small movements done in a sometimes slow and sometimes sudden manner. His releasing of energy (fajin) was hard and crisp, accompanied with sudden sounds. The spirit from his eyes would shoot out in all directions, flashing like lightning. Combined with a sneer, a sinister laugh, and the sounds of "Heng!" and "Ha!", his imposing manner was quite threatening. Shao Hou taught students to strike quickly after coming into contact with the opponent, wearing expressions from the full spectrum of emotions when he taught them."

You need to ask your instructor or one you are learning from, where are these methods, and application. Why is he teaching pushing, and competition push-hands. Remember, taiji is battlefield art, but as large number of people learn it would not even hurt a fly.